Analytical solutions for a surface-loaded isotropic elastic layer with surface energy effects
Analytical solutions for a surface-loaded isotropic elastic layer with surface energy effects
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DOI：
10.1016/j.ijengsci.2008.12.013
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发表时间：
2009-11
影响因子：
6.6
通讯作者：
Xujun Zhao;R. Rajapakse
中科院分区：
文献类型：
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作者：
Xujun Zhao;R. Rajapakse
考虑表面（界面）能量对固体材料弹性场的影响在固体力学的几个现代问题中有应用。Gurtin-Murdoch连续统模型[M. E. A. I. Gurtin默多克，大配给。机械肛门57（1975）291-323; M.E. Gurtin，J. Weissmuller，F. Larché，Philos.Mag.A 78（1998）1093-1109]，考虑表面能效应，用于分析粘结到刚性基底的各向同性弹性层的弹性场。用残余表面张力和表面拉梅常数表征了表面性质。用Fourier积分变换和Hankel积分变换表示的体相介质的通解分别用于二维和轴对称三维问题的求解。广义杨拉普拉斯方程的表面产生一组非经典边界条件的当前类的问题。本文给出了一个层弹性场的显式解析解。层的解决方案是专门获得半无限域的封闭形式的解决方案。选定的数值结果显示表面弹性常数和层厚度对应力和位移的影响。
Consideration of surface (interface) energy effects on the elastic field of a solid material has applications in several modern problems in solid mechanics. The Gurtin–Murdoch continuum model [M.E. Gurtin, A.I. Murdoch, Arch. Ration. Mech. Anal. 57 (1975) 291–323; M.E. Gurtin, J. Weissmuller, F. Larché, Philos. Mag. A 78 (1998) 1093–1109] accounting for surface energy effects is applied to analyze the elastic field of an isotropic elastic layer bonded to a rigid base. The surface properties are characterized by the residual surface tension and surface Lame constants. The general solutions of the bulk medium expressed in terms of Fourier integral transforms and Hankel integral transforms are used to formulate the two-dimensional and axisymmetric three-dimensional problems, respectively. The generalized Young–Laplace equation for a surface yields a set of non-classical boundary conditions for the current class of problems. An explicit analytical solution is presented for the elastic field of a layer. The layer solution is specialized to obtain closed-form solutions for semi-infinite domains. Selected numerical results are presented to show the influence of surface elastic constants and layer thickness on stresses and displacements.